Backward-wave amplifier



Oct. 4, 1960 2,955,226

M` R. CURRIE El' AL BACKWARD-WAVE AMPLIFIER Filed June 13, 1955 8 Sheets-Sheet 1 OU TPUT SVG/VAL l/VPUT S/GA/A A sAcA/waeo WAVE PHAseyacc/TY 14,

, Q/200,0 yacc/ry l@ :E IEI E Oet. 4, 1960 M. R. CURRIE ErAL 2,955,226

BAcKwARn-WAVE AMPLIFIER Filed June 13, 1955 8 Sheets-Sheet 2 GA//v (da) I'Il5 El O .4 L?. L6 2.0 2.4 2.5 3.2

VELOCITY PAPAMETEQ b I., Arma/EPS M. R. CURRIE ET AL BACKWARD-WAVE AMPLIFIER Oct. 4, 1960 8 Sheets-Sheet 3 Filed June 13, 1955 OUTPUT mwa/w caff/e cf L/OH/V A2 MMA/PV INVENTOR.

Oct. 4, 1960 M. R. CURRIE ETAL 2,955,226

` BACKwARD-WAVE AMPLIFIER Filed June 13, 1955 8 Sheets-Sheet 4 IN2 u IUUMLl Mmmm/f A?. 0022/6 Oct. 4, 1960 M. R. cuRRlE ETAL 2,955,226

BACKWARD-WAVE AMPLIFIER Filed June 13, 1955 8 Sheets-Sheet 5 IN V EN T0125` Oct. 4, 1960 M. R. cuRRlE ETAL 2,955,226

BACKWARD-WAVE AMPLIFIER Filed June 13, 1955 8 Sheets-Sheet '7 :E I En- E-l: JU/WV A7. WMM/5?? INVENTORS BWM TME/VWS Oct. 4, 1960 M. R. cURRlE ETAL 2,955,226 BACKWARD-WAVE AMPLIFIER Filed June 13, 1955 8 Sheets-Sheet 8 United States Patent O 2,955,226 AcKwARn-WAvE AMPLIFIER Malcolm R. Currie, Beverly Hills, and John R.-Whinnery, l Orinda, Calif., assignors toThe Regents of the Uni` versity of California, Berkeley, Calif., a corporation of California vFiled June 13, 1955, Ser. No. 514,843

2'1 Claims. (Cl. 315-16) This invention relates generally to backward-wave amplifiers, and more particularly to a cascade backwardwave amplifier.

Traveling wave amplifiers and oscillators generally comprise a periodic (slow-wave) structure along which the electromagnetic wave to'be amplified is propagated.

Patented Oct. 4, 1960 Y varying the beam voltage. As an oscillator, the tube is The periodic structure may, for example, comprise a helical winding. In such structures the wave travels along the structure at the speed of light, but the phase velocity in the axial direction is dependent upon the configuration of the structure, and generally corresponds to the velocity of the electron beam.

-An electron beam is projected along the periodic structure and adjacent thereto. There is coupling between the electron beam and the electromagnetic wave. Thus, there is continuous interaction between the wave traveling along the helix and the electron beam. As a result of the Interaction, energy is transferred from the electron beam to the electromagnetic wave-thereby amplifying the wave.

This is analogous to a breeze blowing over water', thereby"- creating and increasing the amplitude of waves.

Two types of prior art ltraveling wave apparatus exist. In one the electromagnetic wave is introduced at the electron gun end of the periodic structure and the amplified wave is extracted at the collector end. Because of Ithe periodicity of the structure a periodic axial eld is set up by the electromagnetic wave. Due to this periodic field, certain lof the electrons traveling in the electron beam are slowed down while others are speeded up. If the speeding up land slowing down of the electrons were exactly equal, no amplification/could result. It turns out however that the two Vquantities are not exactly equal. There is bunching around the -slow moving electrons, thus reducing the mean velocity and hence the kinetic energy of the beam as a whole. This increment of kinetic energy is transferred to the traveling electromagnetic wave and results in the wave being amplified. In this ty'pe of tube the phase velocity and energy transfer are in the same direction as the motion of the electron beam.

The second type of traveling wave device is sometimes referred to as backward-wave amplifier or oscillator. In this device the electromagnetic Wave is introduced at thecollector end Iand the amplified signal is removed at the gun end. Thus it is seen that this type of circuit supports a backward wave. Here again the wave is characterized by a phase velocity which is in the direction of current flow. The direction of energy transfer (group velocity) is in an opposite sense. Since it possesses a phase velocity which is in a direction of electron current and which is approximately synchronized Awith the beam velocity, a portion of the kinetic energy ofthe electrons will be converted to wave energy by an interaction process which is identical with that described above.

The principal diiference between the two types ofcircuits is not a fundamental difference in electronic interaction, but is a difference in the direction of energy ilow. The backward wave device is inherently likewise electronically tunable over a 2 or 3 to 1 range in frequency with the conditions for regeneration automatically produced by the feedback nature of the electronic interaction.

Backward-wave 'amplifiers have several serious disadvantages. When reasonably high gains are required, the beam current must be nearthe values where oscillations start. Thus, when operating at high gains, stable operation is difcult. lf the couplings into and out of the helix :are imperfect, the internal rellections may cause the value of the current to fluctuate periodically about a smooth curve -as the frequency changes. This causes sharp gain fluctuations or even excursions into the oscillation region of the amplier. A further 4disadvantage of this' ty'pe of l amplifier is that there is aV direct feedthrough path between the input signal and the output signal.

It is a general object of the present invention to an improved backward-wave apparatus.

It is another object of this invention to provi-de back- Ward apparatus which is inherently stable in operation.

It is a further object of the present invention to provide backward-wave apparatus which gives relatively high gain with operating currents which )are substantially below the start oscillation current.

It is a further object'of this invention to provide backward-wave 'apparatus in which the off-signal rejection isv high.

It is still a further object of the present invention'to provide a traveling wave apparatus in which the bande width may be controlled.

IIt is still a further object of this invention to provide backward-wave apparatus in which `the operating characteristics can be made to vary smoothly with frequency, and which may be designed for almost constant gain over a large frequency range. 'f These and other objects of the invention will appear more clearly from the following description taken in conjunction with the accompanying drawings.

Referring to the drawings:

Figure 1 is a schematic model of a backward-wave cir- Y Figure 2 shows the build-up of current modulation and circuit eld as a function of distance in a backward-wave circuit;

Figure 3 shows the parameter CML) wave amplifier;

Figure 5 shows the gain of a cascade backward-Wave amplier as a function of the velocity parameter;

Figure 6 shows the gain of a cascade backward-wave amplifier as a function of current;

Figure 7 is a schematic model of a cascade backward--Y Figure 8 is a schematic model of a cascade backwardprovide wave ampli-fier in which the modulator and demodulator sections are separated by a drift tube;

Figure 9 shows the etect'of the drift region on the gain of` the-:cascade'backward-wave lampliiien Figure 10 is a schematic model of atcascade,backward:Y wave amplier in. which the' modulator andtdemodulator sections are separated by a oating helix;

Figure 11 shows the minimum noise .figure of acascade backward-wave rampliiier',

Figure 12 `is aside elevational view partly in' section of a cascade backward-wave amplifier;

Figure 13 is across-sectional view showingthe-electron gunemployed inthe cascade backward-wave amplif.. tier of Figure 12;i Y

Figure 14 is4 a sectional view takeiralong` the linesv 14--14 ofFigure :12;

Figure 15. showsza tuning` curve for abackward-wave cascade amplifier;

Figurev 16. showsaoscilloscope; traces of. output power as'A a cascadezbackward-wave amplifier vis swept in voltage; f

izedourrent at different frequencies;

Figure :18 is a compan's'oniof measured'and. theoretical.` gain as a function of `frequency fonan experimental cascade backward-wave.ampliiier;r

Figure.19 shows curves of the beam to maintain constant gain;V

Figure 20V is 4a curve of voltage gaintimes bandwidth for a cascade backward-wave amplifier;

FigureV 2l showsv theV effect oistagger tuning on the bandwidth of a typical cascadeiampliiier;

VFigu-re22 vshows aschematicV view of a cascade ampliiier which: employsv a zigzag waveguide periodic struc-Y ture;

Figure 23. shows aschematic View of another cascade backward-wave amplifier which employs a loaded. waveguide periodic structure; and

Figure24 shows another cascade-backward-wave.amplicurrent necessary er in which theperiodic structure comprises AaV ridged.

waveguide with traverse slots.

Figure 25- showsa schematic view of=a backward-wave amplier which employs a grid for modulation and` a periodic structure for demodulation;

Figure 26 shows a schematic View of a backward-wave amplifier which employs a cavity for modulationand-,a

periodic `structure for demodulation; and.

VFigure V27 showsv arf-schematic view of. a backward-wave: amplier which employs a periodic structure for modulation and a cavity for demodulation.

In order to more fully understand backward-wave-.interaction, the model shown inrFigure l'will -be analyzed@ A transmission-line approach is used, the equations of motion and continuityare linearized V(smallsignal), and motion only in the z direction is allowed. The beam is assumed to possess an'arbitrary'initialcurrent and velocityimodulation (bunchingfas it enters the circuit at 1:0; Time dependents of the radio frequency quantities is assumed..

to be of exp'wt). u Y

The relation between R.-F. convection currents i(z) on the electron beam and thelongitudinal (axial) field on the slow Wave circuit E ("z) is:

ita) d'(z) Ligen@ a;

@fue me);

Similarly, the mod ed telegraphers equation, giving cou-V plingbetweenthe circuit and beam,.is:l

Figure 17 shows .curvesof gain as alrfunction oinormalv C=gain parameter, I=the propagation constant.

In the absence of the electron beam the circuit wave propagates as exp(jwt-1`0z).

A solution for the composite beam circuit model involves the simultaneous solutionsof the above equations.

`E01) and i(z)- arethen` solutionsof fourth-order linear diierential equations. The associated constants in the solutions: arenlixediby4 four; independent boundary: conditions. Two` ofl theseconditions .pertaini to the. beam and two to thecircuit. The-current and`4 velocit-y modulation can be independently specied at z=0 and? the applied circuit field at -zf-L is known.; The -remaining constraints can be taken as a matched circuit termination at one end. The solutions'vcanlbe expanded in Iterms of exponentials (i.e., four Waves).

Employing methods described in Traveling-Wave Tubes by Pierce, publishedfinfslQSOby'DJ Van-.Nostrand tial waves. Assuming linearized definition .ofi Riflircur rents,A conservation: of charge; thati theaphase; velocities of the perturbed Waves are4 close-.tothe D.C. bearnvelocities; and1that...the-.r.circuit. iszmatched ati one zend, the complete solutionsforr thez-outpu "3* quantities.' cani be written:

The coeiicients are functionsv ofthe D.C. conditions of the beam, velocity b, circuit loss'd, space-charge QC and circuit length. The following functions are dencd:

Q: ,-izrN-z (552 61:2) e21rCN(i-i5k)' where; i, j, k aretaken as cyclic permutations ofil', 2, 3, N :number of electronic wavelengths in circuit length L,

QC=the space charge, parameter, b='beam velocity, d :circuit loss, 10: .-C. linear charge density n`=incremental propagation constant, uo=D.'-C. velocity, I0=inp ut.beam current, V=input field, D.C; beam potential:

vThelinear: relationships, Equations 3" through 5, express the output .quantities in rterms .of velocity,.current alldl'-wliibh are impressedonV the system. 'Ille-co-y efficients consist `of a general matrix for applications in v the succeeding calculations.

The backward-wave amplifier previously described has a smooth beam injected from the electron gun directly into the interaction space. No R.F. or velocity modulation exists on the beam at the gun end of the circuit. As a result of the interaction process, the circuit field builds up from its initial impressed value at z=L to a maximum value at z=0, thus being amplified. The modulation (bunching) induced on the beam increases in magnitude in the direction of the electron ilow, thus giving the greatest bunching at the collector end of the stream. When the feedback Within the circuit is Sullicient, the amplifier goes into oscillation.

The power associated with the circuit is:

and the power gain can be written as:

For a fixed amount of space charge (QC) and circuit loss (d), it is possible to adjust the beam velocity (b) and the electrical length of the circuit (CN) so that the denominator in the 'above expression vanishes. This condition of infinite small-signal gain is unstable and is taken as the point at which 'the amplifier becomes an oscillator.

An amplier of this type is capable Vof yielding very high values of gain. Because of the Iregenerative action, the tube characteristically possesses a very sharp frequency response. The limitations of this amplifier have been previously described. Briey they depend upon the lack of separation between the input and output circuits and the fact that the ampliiier must be operated near` the oscillation region to obtain maximum gain.

Analyzing the same circuit but paying particular attention to the modulation (bunching) `on the beam, the following equations may be derived from Equations 4 and 5 for the R.F. current and velocity modulation which is induced upon the beam as a result of the interaction process.

Referring particularly to Figure 2, the R.F. current and iield are shown as functions `of distance for the special case of zero space charge and circuit loss. The curves are for a current of about 87 percent of the starting value and for a value of beam velocity (b) which optimizes the gain of -the device as an amplifier. The curves emphasize the fact that where the current modulation is weak, the circuit field is strong and vice versa. This is inherent in the nature of the interaction and differs markedly from the forward wave interaction.

It is of interest to examine the nature of the modula- E in 0(2): Ein

tion just as it leaves the interaction space. A descripftive parameter is the dimensionless ratio l (z/LCN) www JX 10 o-(L) is shown in Figure 3 as a function rof length of circuit (CN) for space charge (QC) equal zero, circuit loss (d) equal zero, and optimum beam velocity (b).- As the effective length CN of the interaction space increases the magnitude of r(L) also increases. The current modulation leads the velocity modulation (in the time sense) by an angle greater than 100 degrees indicating that there is power carried by the electron beam. This is in contrast to a lglystron in which the angle is 90 fers considerably from the case of the forward wave amf ti degrees and no R.F. power is the limiting case of large QC,

Where, in this case Y 'bE\/4QC (l2) Therefore, increased current density causes the phase angle between current and velocity modulation at the end of the interaction space to 'increase and lff(L)| to decrease.

Referring again to the curve of Figure 2, it is seen that where current modulation is weak the iield is strong. This is inherent in the nature of the interaction and difplier. This suggests that backward-wave interaction is a relatively inefcient process.

It is desirable to secure stronger reciprocal action between the beam and circuit. We have found that a stronger reciprocal action may be obtained by placing initial modulation on the beam so that the interaction can commence with relatively large R.F. energy associated with both the electron beam and the circuit (wave).

Referring again to Figure l, consider the case inwhich the beam is injected into the interaction space with both velocity and current modulations whose magnitudes and relative phases are arbitrary. Assume further that the collector end of the circuit is passively terminated in a matched load. Let us now consider the circuit eld which is induced on the helix, in particular its value at the output terminals. From Equations 3 and 10 where vin and am describe the input modulation.'

Since the induced field is strongly dependent upon the parameter am and hence on the nature of the system employed in the original modulation of the beam, We shall examine several specic cases. First let us compare the backward-wave circuit with the output cavity of a klystron amplifier. In a simple klystron amplifier, the cavity is located at a point of maximum current modulation along the beam. The bunched electrons then induce a current flow in the cavity walls and excite it to resonance. An equivalent shunt resistance of the cavity can be defined which relates the power delivered to the resonator to the fundamental convection current component in the beam,

2 @Fi-f3 14) A ligure of merit for the cavity is usually taken as the ratio mgamxbandwidth 15) An upper limit for this ratio is roughly with Rsh approximately equal to 100,000 and Q approximately equal to 1000. Rsh can be increased at the expense of bandwidth, and vice versa.

-Now let us consider the situation in which the klyst-ron cavity is replaced by a backward-Wave structure. The' two arrangements are similar in several important` respects. Both devices are narrow-band; both absorb energy from a bunched beam. The systems are on one. hand resonant and on the other hand strongly regenera-, tive in nature. yFor contrast it is of interest to dene an effective shunt resistance-for the backward-wave circuit for the case of pure current modulation at its input and to compare the resulting figure with that obtainable carried by the beam. For

from a klystroncavityi. From Equations 6.and. 13 the following expression is obtained,`4 3.,.

(neufs-(v) @im 16) Substitution of some conservative parametersV Y(l/.-500v volts', ID-3 ma., K-5 ohms, luf-0.7150 into the above relation indicates that.an eflective shunt impedance of 105V ohms can easily be obtained in practice.' It will be presently shown .that the corresponding Q :in thiszregion' of operation vis-typically ofthe order`ofl409. 'As in the case of a klystron (Rsh)eff can beincreased at theexpense of bandwidth. A length of .backward-wave circuit therefore represents. a conceptual' improvement" overa` re-entrant-type resonator on the basis oftheir relative guresofmerit. This is not surprising when the cumulative nature ofthe distributed interactionis considered; howeven. it does illustrate the eiectiveness of a backward-wave demodulator (de-buncher) in extracting energy from a hunched beam.

From: these considerations it is seen, principle, an

ampliiier can be constructed which .utilizes a re-entrant cavity to modulate the beam and a periodic circuit as' the output structure. Such an amplifier is entirely feasible and would' appear to possess some advantages:

The denominator in the expression for the field at the output of the demodulator is. exactly the same as that which appears in the gain expression for a simple backward-wave amplifier. This implies that for identical circuits, the condition of instability (i.e., start-oscillation) occurs at the same point and is independent of externally applied fields.

Referring particularly to Figure 4, we have shown a novel cascade backward-.waveamplier- The amplifier comprises generally an electron gun which projects a beam of electrons to a collector. rIwo periodic structures are located adjacent theV beam whereby a wave traveling along the structures interacts with the electron stream. The structures shown are helices,V but it is to be understood thatl the structuresmay comprise any periodic structure (slow-wave structurelcapable of propagating a wave` having a slo'w axial velocity. The input signal is intro-Y duced at' the collector endv of the periodic structure nearest the electrony gun and serves to modulate (bunch) the electron beam. The modulated electron beam then interacts withtlie secondtperiodic structurewhich actsl as a demodulator; althoughthe electrons mayhave a` greater" modulation'when they leavethe section than' when they*` enter thel section: The outputV signal is removed at' the gun end of the second periodic structure.

Assuming that the two helices are completely isolated oneV from the other, and that nocoupling between them exists in the absence of the electron stream, the power output of the second helix is given by the expression 1'V yg in* Y normanni Pout'-(2K)1/3(I0) ip D(vm)2i `A2l2 Where the added subscripts (2)1 denote quantities pertaining to the second helix and (amb describes the beam modulation at its entrance. From Equation 9 the velocity modulation. at theoutpnt of the Aiirst helix is given by and, in this case, with. no.V separation' between. circuits and no velocity jump,A thecontinuity'of velocity and-cur rent is expressedby (O'Ons)1=r('in)2, (PoVuot)r=(Pn1/m)2 vC179) The gain expression for the severed-circuitamplier becomes. e f

The simplest case results when both helices are the same physical length (it has been .implicitly assumed that they.

are identical in allother respects). Thisis also the-case of greatest interest. For operationatV a specified fraction ofstartingcurrentiv maximum gain willbe obtained for, equal circuit lengths.- In thisV case Vthe over-allgaiir is .velocity and frequency, Figure 5 illustrates the reciprocal relation, between gain and bandwidth. From thedeinifv tion of' b t 1 m 1 er" Abg C UD N f so that the velocity width Ab is proportional to the bandwidth. For aitape helix the phase velocity of the dominant -backwardfwave liarmonicis o?" Drk@ where:

tb=pitchiangle of .the helix, ka=ratio of circumference to free-.spacewavelengtn D=dielectricloading factor.

Therefore N Mica). Mza (1i-ka) (24) and the bandwidth becomes AfgCfQ-k-g A1` 25) where Ab is interpreted as the spread of the gain curves at the half-power points.

An equivalent Q of theampliiier can be deiined aga@- an equivalent Q: of approximately 400' willbe realized.' A higherY Q at a` given vgain. level can 'be obtained by. decreasing the beamehelix coupling andl going to longer' lengths of helix (at the same CN). VAlternately, operation at higher `beam voltages, lowerecurrents, and-theuseY of moredispersiveA backward-wave circuits' could be employed. Y Y Y For the case ofv largespace charge ield at the output of the demodulator section can be written if 1f CN Enum: 2C2(P0)m)z bilan The over-ali gain then becomesapproximately fg 4 I2 m] G tan [2 In) (.28)

Referringrparticularly to Figure 6', thev gain .of thel:

severed-helix. .amplienii optimized .with respect.. toVv b, is

i (QC), the circuit shown as a function of Vcurrent for the limiting cases of large and small space charge (zero loss). The curves are universal. AThat is, the starting current Ist `can be separately calculated as a function of frequency in any specific case. The rapid rise of the curves from the regionv of negative gain indicates the strong interaction which occurs in the demodulator. A curve for Llr--l/zLz illustrates the desirability of using circuits of equal length.

A comparison of the characteristics of the idealized severed-helix tube with those of the simple backwardwave tube have previously been given. A typical calculation (I=0.7Ist, QC=0, d=0) shows that where the latter device produces a gain of ll db, the gain of the modulator-demodulator configuration is approximately 32 db. `In order to put the comparison on a fairer basis, it should be recognized that the composite system which includes two circuits each have an electrical length equal. to that of the single circuit in the conventional backwardinduced during the beam transit through the first circuitis immediately placed in the region of maximum field on the second circuit. An enhanced reciprocal interaction between the beam and the circuit results, thus leading to the improved results observed.

The idealized model of the severed helix could not be realized very closely in practice. Two circuits placed immediately adjacent each other would prohibit "good input and output matching and their fringing fields would not yield the high degree of isolation which is desired.

In a more practical model the circuits are separated by an arbitrary structure. A general configuration of this type is shown in Figure 7. This structure again includes first and second periodic structures which act as modulator-demodulator sections coupled to anelectron beam. A transducer is inserted between the two sections and serves not only to isolate the input and output circuits, but also to transform the velocity and current modulation which exists on the beam at the end of the first section so as to optimize its output signal. `In the general case, the transducer can consist of any combination of propagating or non-propagating circuits.

'I'he simplest transducer section can be of the type shown in Figure 8 which consists merely of a drift tube.`

This constitutes an analogy with the klystron, although the drift tube here is not essential to the bunching mechanism. The effect of the drift tube on the over-all gain can be simply determined under the assumption that only one mode is excited in this region by the input modulation (denoted i,a and vn). In this case the transformation to new values ib and vb can be described in terms of the space-charge waves of a single mode; the drift region can be regarded as a passive and lossless two-terminal pair network. 'Ihe validity of the above assumption depends upon the particular geometry of the structure. For a helix circuit and a hollow beam, such an analysis can be verified experimentally.

'Ihe output modulation is related to the input modulation by the following equations Fripes .9a-j? sin au] (29) povb=povalcos 6., -jg sin 0.,] Y v(30) where A .,:uad (matan length of drift tube) (31)" ot. da=rwn C cu i 0'0- 251;

where The first factor in Equation 36 is the gain of the idealized severed-helix tubes; the factor HH* represents the eect of the drift region on the over-all gain of the device. Referring particularly to `fFigure 9, some representative curves of HH* (expressed in db) `are given as a function of drift tube length for various a0. Although these curves are for operation at 70 percent of starting current, it is found that they do not change significantly with the 'ratio IO/Ist. It is apparent that a drift 'tube can increase the over-all gain for magnitudes' of a0 either much greater or much smaller than unity. The former condition can only be met at the higher frequencies (e.g., X-band and with the beam grazing the drift tube so as to lower the value of R.

For typical operation of a helix-type backward-wave tube of S-band, tro may have a Value near 1. In this range nearly all drift lengths result in a subtraction from the net gain. However, the magnitude of gain is often only of secondary importance -in such `a tube. For example, in the `application of the tube as a swept amplifier, it may -be more important to maintain reasonably constant gain as 1a function of frequency at `a constant value of beam current. The gain of the severed-helix tube (at small QC) is la function only of normalized current (I0/Ist). Since Ist generally increases with frequency, the gain at constant current will decrease at higher frequencies. The choice of drift distance therefore lends an additional degree of freedom to the design of the tube. In particular, referring to iFigure 9, it is seen that this region can be made to compensate for the above effect and the over-al1 gain can be made constant with frequency. This compensating action was observed in an experimental amplifier to be presently described. In this sense, the drift region can be regarded as a gain equalizer.

In Figure 10 we have shown -another simple transducer section 1-1 terminated at each end in lossy match 12 and 13. By analogy to the iioating cavity klystron, this configuration is termed the floating helix amplifier. In the limit, this configuration may consist of an arbitrary number of floating circuits between the modulator and de-modulator with each contributing to the over-all gain 11 to the input and output circuits, the over-all gain is. given by The factor Il* expresses the contribution of the floating circuit to the gain of the idealized model. Numerical calculations for small QC show that at l/Ist=tl.5 the gain is increased by about 9 db and, at IO/Ist=0.7, the new element adds about 19 db. Calculations for unequal circuit lengths or multiple floating circuits can be readily formulated in matrix notation' based on the linear relationships, 4 :and 5.

In considering the application cf the cascade backward-wave ampl-ier as a small-signal device, it is important to know the noise figure', i.e., its capability of detecting extremely low signals. The minimum detectable signal is limited by random fiuctuations of the electrons and the conversion of these fluctuations to noise power on the circuit at the tubes output. A theoretical minimum noise figure for conventional traveling-wave tubes has been calculated recently. In Figure ll`, the minimum noise iigure has been computed for various values of circuit loss d asV a function of space charge QC. Certain features of the curves are worth comment. For zero loss the minimum noise figure is 4exactly the same as for a conventional forward-Wave amplier, namely F=1+(0.9265)2-6 db l 38) However, `the noise figure in the-backward-wave case is much more strongly dependent upon circuit loss than' that of a forward-wave amplier. Moreover, in the latter case, Fmm can be lowered by decreasing the value of d over only Vthe rst several wave-lengths ofV circuit; for the backward-wave circuit, d must be minimized -over its entire length.

ln each of the cases the curves were computed for three lengths of drift tube (0, ls'yq, l/vyqlan'd 50:-1. Exactly lthe same values of Pmm were obtained in each case. Thus, at high gain, the noise iigure isV determined only by the parameters of the modulator section (if the thermal noise of the output circuit ,isV neglected). The signalJto-noise' ratio is iixed as the beam leaves the modulator. Operation at low` gain levels indicate minimum noise figures slightly below those shown in Figure 1l.

Referring particularly to Figures 12- and 13 we have shown a two helix backward-wave amplifier which incorporates our invention; The amplifier comprises genorally an evacuatedV glass envelope 21. An electron gun 22, to be presently described, is disposed at one end ofV the envelope and a collector 23 having cooling iins 24 is disposed at the other end and serves to collect the electrons. A first helix 26 is located adjacent the gun and a second helix 27 is located adjacent the anode. A drift tube 28 is interposed between the helices. As previously described, other types of transducers may be included between the helices and serve to contribute speci-al characteristics to the beam 'as it travels through the region. In certain instances, it maybe possible to eliminate this region entirely and. place the helices adjacent to one'another.'

The input signal is introduced at the collector endl 29 at the tirst helixv and is amplified as it` travels towards the gun end of the tube. The ampliiied signal maybe dissipated in* a helix termination or the yamplified signal may be removed. .As shown, thel end of the" helix adjacent the gun is connected to an:V external coaxial:V line t`oprovidefor measuring the amplified signal' or connection to external attenuating means. It is to be understood of course that in certain applications this end of the helix need not be brought out, but may be terminated within the tube by placing aquadag or other suitable attenuatingV material on the envelope or on the turns of thehelix.V y

As previously described, when a signal is applied to the helix, a wave travelingalong the helix interacts with the electron beams and tends to bunch or modulate the electron beam. The modulated electron beam then passes through the drift region 28 (although this is not essential to operation), and into a second helix or other suitable slow wave circuits which interact with the backward-wave.

The second helix may have its two ends brought out. The output signal is taken from the gun end of the second helix, with the collector end of this circuit match terminated as previously described with respect to the iirst helix.

In the discussion which has preceded and in the succeeding discussion, the tirst helix is referred to as the beam modulator (or buncher) and the second helix will be referred to as the beam rie-modulator (or debuncher), since it extracts energy from the beam. It is to be understood of course that although the second helix extracts energy *from* the beam, it may leave the beam more hunched and spread out in velocity than before the beam enters the helix.

Generally a transition from `a coaxial line to a helix introduces large standing Wave ratios (reliections). It is desirable to provide a suitable tapered connection or a connection of the type shown. A ring E16` is placed about the tube and interconnects with the outside of the coaxial line. Thus, the transition is gradual from the coaxial line to the helix. I

It is worth noting that in order to maintain a closer balance of the helix dimensions and to match the two` sections, special precautionsshould be taken in forming the helices.

adjacent one another on a mandrel. 'Ihe resulting gap between successive turns may have a wire wedgedr therein to form a solid cylinder around the mandrel. The

having flutes 34. VThe helices are then titted snugly intothe uted envelope and are relatively free from dielectric loading.V

The hollow, beam electron gun shownA in Figure 13 may be of the type disclosed by Pierce in Theory and Design of Electron Beams, D. Van Nostrand Company, in 1954. Generally, the gun has a ceramic base 36 which. serves to mount the grid elements 37 and 38- which are formed with annular slots.39 and 40 respectively. The cathode which may be made of nickel is also mounted on the ceramic base.

The electrons emitted by the cathode are generally in the for-m of ian annular beam and pass through the slot 39 into the helix region to thereby interact with the helix. The tube is enclosed within a magnetic field structure which provides a longitudinal magnetic line field which hold the electrons in a straight path to thereby give the desired cylindrical beam. This type of beam -gives maximum interaction.

A cascade backward-wave ampliiier of the type shown i in Figures 12-14 was constructed for S-band. The tube utilized a hollow beam gun, tape helices for the back- One method which may be employed isv worth mentioning. The two helices may beV wound envelope may Aalso require lspecial A heater current is supplied along the line 42 to indirectly heat thecathod'e.

ward interaction structure, a drift space between the helix. Input and output helices were each 51/2 inches long, 0.45 inch inside diameter, and had 0.125 inch pitch. The drift tube was 21/2 inches long (l plasma Wavelength at the center of 2-4 kmc. band). All four ends of the helices were brought out to type BNC angle connectors. The hollow beam used to secure interaction with the backward wave component had a radial thickness of 0.030 inch and it was separated from the helix by approximately 0.025 inch. The measured isolation between the two helix sections was greater than 50 db.

Referring to Figure 15, the measured tuning range of the amplifier is shown. The tuning range is from 2,000 mc. to 4,000 mc. with accelerating voltage variations from 270 to 4,000 volts.

Figure 16 shows an oscilloscope comparison of the gain for the two helix tubes with that for one of the helices operating as a single helix backward-wave amplifier with the same ratio of operating to starting current. The two traces were recorded successively with the same detection system and represent power output vs. beam voltage as the tube was swept over a frequency range centered at 3,000 mc. A small gain spike was taken from the gun end of the signal launcher, and so represents the gain of the single helix backward-wave `amplifier. The base line of this trace represents the average power of the signal generator. the `gain is a region of negative gain in which the interaction has become de-generative. Other maxima and minima of the interference pattern decrease in amplitude as one departs from synchronization with the circuit wave. The large response curve was taken yfrom the gun end of the second helix and shows a large land very clean response for the cascaded helix amplifier. Since no direct feed-through path exists-from input to output, the reference line on this trace represents essentially zero power.

Figure 17 shows measured values of gain vs. current for the tube, taken at several frequencies. Measurements were taken with bolometers located both at the output of the composite tube and at the output of the first helix. Tuning stubs were employed but were not adjusted during measurement for a particular frequency. Considerably greater apparent gain could be obtained by deliberate mismatching so as to reinforce the output signal by int ternal reflections. One of the theoretical curves shown for comparison is that for a single helix amplifier. This shows a much smaller gain for a given current. The other theoretical curve is the calculated curve for a two helix tube with no drift space between helices (denoted severed helix tube). The calculations previously presented indicate that the effect of the drift tube is to subtract increasingly from the over-al1 gain `as the frequency is lowered.

lFigure 18 shows gain vs. frequency for two values of normalized current. The theoretical curves (dotted) do not take into' account the effect of the drift region.

Close agreement between the calculated and measured values is shown, but as the calculations neglectthe finite circuit loss and space charge eects, this should not be taken too literally.

Figure 19 shows the required variations in current as functions of frequency for constant gains of 20 db and 30 db. This serves to illustrate the role of the drift tube as again equalizer vand the bexibility that this element lends to over-all design.

The frequency bandwidth was measured at several frequencies and gains; measured results are shown in Figure 20. The gain bandwidth product is a strongly increasing function of gain. The gain bandwidth product of a single circuit backward-wave amplifier is much less dependent upon gain and is almost constant. Thus, the bandwidth is largely fixed by the parameters of the input circuit; the increased gain bandwidth product for the The dip to the right of `14l cascade configuration is for a given value of beam current.

The noise figure was measured at one point and was about 24 db. This is in thesame range as for the typical forward wave traveling wave tube amplifier when n0 special effort is made to reduce the noise on the electron stream (e.g., by a means of wvelocity jumps); it is also in fair agreement with calculated noise figures assuming space charge limited flow from the cathode to the first helix and taking into account only the effect due to velocity fluctuations of the potential minimum.

The bandwidth of the cascade amplifier may be varied by stagger tuning the input and output circuits (Le. operating them at slightly Vdifferent potentials so that synchronism between the circuit wave and the beam velocity occur at slightly different frequencies in each section. Referring to Figure 21, an oscilloscope trace of a staggered tuned amplifier is shown. To obtain this curve, the input frequency was swept fro'm 2 kmc. to 3 kmc. with a backward-wave oscillator. The traces display output power vs. frequency.V With the modulator and demodulator circuits synchronized the bandwidth at 2.7 kmc. and 19 db gain 'was 10 mc. With a 30 volt potential difference between the helices ,the gain dropped to about 11 db, and the bandwidth increased to 35 mc. The response resembles that of two tuned circuits which are over-coupled. For smaller voltage differences it is possible to increase the gain bandwidth product somewhat currents and yet give large power outputs.

Such an experiment was carried out with the above described tube and oscillations started at 4 milliamperes current. At 5 milliamperes the power output was 1 Watt and the efliciency was 12%, as measured. In such a circuit the phase of the feedback signal is extremely critical. v

In Figure 22 we have shown a cascade backward-wave amplier having an electron gun 41 which projects an electron beam 42. The collector 43 serves to receive the electron beam. The periodic (slow wave) structures 44 which propagate the waves are of the zigzag waveguide type in which 'the axial phase velocity of the wave corresponds to the velocity of the electron beam. A transducer of the drift tube type 46` isdisposed between the section 44a which serves as a modulator and the section 44b which serves as the de-modulator.

In Figure 23 we have shown an amplifier having periodic structures 44 of the loaded waveguide type. The structures give an axial phase velocity which corresponds to the velocity of the electron beam, thereby allowing interaction between the electron beam and the backward phase. In Figure 24, another amplifier is shown in which the periodic structure is `of the loaded waveguide type.

It is to be understood of course that the periodic structures which have been illustrated and described are illustrative only. Any periodicrstructure capable of propagating the Wave with the proper axial phase velocity will be suitable for use in the cascade backward-wave amplifier. Further, one type of structure may be used in the modulator section and a different type of structure in the de-modulator section. Thus it is seen that the invention is not limited to particular periodic structures, but that structures capable of modulating and `demodulating the due to greatly increased gainv wave then interactswith a periodic structure which, for example, may be a helix 54. The periodic structure serves todo-modulate the beam andprovide an amplied'output at the gun end of the structure.

In Figure 26, a cascade backward-wave amplifier having an electron gun 56 which projects an electron beam 57 `to the collector 5S is shown. The beam is modulated by means of the cavity 59 andtravels through a drift region 61. A periodicy structure, shown as a helix 62, interacts with the electron beam and serves to de-modulate the beam and provide 'an amplied output at the gunfend of the periodicstructure.

In Figure 27 weV have shown an ampliiier similar to that of Figure 26 in which the cavity is placed adjacent the collector end and the periodic structure, adjacent the gun end. Thus Ithe periodic structure serves as the modulator and-,the cavity as the de-modulator.

Operation of the, ampliiiers shown in Figures 25 through-27 Yissimilar to that` previously described. r.that is, thebearn is modulated, and a structure interacts with the modulatedl beam to. thereby de-modulate the beam. Thekinetic-energy of the beam is reduced and Van amplitied output results.`

From-the foregoing, it is seen that wek have provided a greatly improved backward-wave traveling-wave arnpliiier tube. In the cascade amplifier described, a relatively high gain-is achieved with operating currents which are far below thestart oscillation current. The slope of the gain-current curve is also muchV smaller.. for a given gain, so that stable operation is possible over-the entire frequency band. Another advantage of the cascade ampliiier which we have-described lies inthe freedom to terminate one end of each section in an internaly reflectionless match. With tapered terminations placedl on the circuit, the operating characteristics may be made to vary smoothly with frequency, and the amplifier may be designed for almost constant gain over a large frequency range.

In a single helix backward-wave tube the inputand output terminals are connected. through theV helix. lnV

the cascade traveling-wave tube, a break is made between the input and output terminals, that is, the helix is severed. Only a. narrow band of frequenciesV whose corresponding backward-wave phase velocities are in approximate'synchronism with the beam.veloc ityY can .be coupled onto the output circuit; other signals are Vsimply dissipated in the lossy terminations of the input circuit. The olif-signal rejection-ofthe cascade amplifier is thereorevery high, whereas a single circuit backward amplilier provides a direct feedthroughpath which must be broken artificially if :adequate cold loss is to be introduced. A further advantage with the cascade amplier described is the possibility of altering bandwidth bystagger-tuning the sections; This results in a iilterwhose center frequency and bandwidth may be varieda electronically.

We claim:

l. A backward wave ampliiier comprising an electron gun serving to project an electron beam, a collector spacedy frorrrsaidy gunfandserving to receive'said beam,

modulatingmeansserving toV receive an input electromagnetic wave and disposed whereby said wave interacts with the beam to modulate the-same, second means serving to support an output wave disposed whereby the wave interacts with the modulated beam to extract energy therefrom and produce an ampliiied output wave at the gunendsofthesame, said second-means compris-- ing a periodic structure serving to support a backward travelling wave with the maximum iieldsoccurring near the electron gun end so that the modulated-beam initially interacts with maximum ields after leaving the modulating means.

2. A` backward wave amplilier comprising` an electron gun serving to project an electronbeam, al collector Vspaced from saidgun and serving'to receive Sad beam, a

first periodic structure adapted to propagate a backward electromagnetic wave corresponding 4to an input signal, said structure disposed wherebythe fields ofthe propagated waveinteract with the electron beam to modulate the beam in accordance therewith, and a second. periodic structure adapted to propagate an output backward electromagnetic wave corresponding to theinput signal, said wave having maximum elds near the gun end of said second structure, said second structure being spaced along the beam from said iirst structure and disposed. whereby the elds of the propagated output wave interact with the beam to extract energy therefrom, said modulated beam initially interacting with the output electromagnetic wave in a regionV of maximum iield whereby to provide an enhanced interaction between the wave and beam.

3. Apparatus as in claim 2 wherein said first and second periodic structures comprise slow-wave structures.

4. Apparatus as in claim 2 wherein said lirst and second periodic .structures comprise helices.

5. A backward wave amplifier comprising an electron gun serving to project an electron beam, a collector spaced from said gun and adapted to intercept said beam, a first periodic structure adapted to propagate abackward electromagnetic wave corresponding to an input signal, said structure disposed whereby the fields of the propagated wave interact with the electron beam to modulate the beam in Aaccordance therewith, input means located at the collector end of said irst structure whereby an input signal may be applied thereto, a second periodic structure adapted to support a backward wave which interacts with the modulated beam to extract energy therefrom, the maximum iields on said second periodic structure being at the gun end of the structure, said second structure being spaced along the beam' from said first structure and disposedwhereby the elds of the propagated wave interact with the beam to extract'energy therefrom, said modulated beam initially interacting Vwith the output electromagnetic wave ina region of maximum field whereby to provide anV enhanced interaction, and terminating means associated with the collector end of said second structure.

6. Apparatus as in claim 5. wherein said rst and'second periodic structures comprise helices.

7. A backward wave amplilier comprising an electron gun serving` to project an electron beam, a collector spaced from said gun and serving to intercept said beam. a irst periodic structure located at the gun end Vof said beam and servingrto propagate a backward wave corresponding to an input signal, input means located atVV the collector end of said structure and adapted4 Vto Vreceive an input signal and apply the same to the periodic struc'- ture, terminating means associated with the gun endlof said structure and serving to attenuateenergy travelling along said lirst structure, a second periodic structure serving to support an output backward wave disposed whereby the wave carried by the structure interacts with the modulated beam to extract` energy'therefrom, the maximum fields on said second periodic structure occurring at the mm ond of the structurevsaid modulated beam initially interacting with the output electromagnetic wave in a region of maximum` field whereby to provide enhanced interaction, output means associated with the gun end of said secondperiodic structure Vfor coupling oirr thel amplified signalV from the-structure, and terminating Ameans located at thecollector end': of the structure and serving lto attenuateincident energy.

8. Apparatus as in claim 7 wherein said periodicstructures comprise cascaded helices.V n

9. Apparatus as in claim 7 wherein said periodlc structures comprise zigzag waveguides. I

l0. Apparatus as in claim 7 wherein said periodic structures comprise loaded waveguides. Y

ll. A backward-wave amplifier comprisingan electron gun serving to project an electron beam, a collector 75.*Spaced from said gun and intercepting said beam, aiirst periodic structure which propagates a backward wave corresponding to an input signal disposed whereby the wave interacts with said beam to modulate the electron beam in accordance with said signal, a second periodic structure serving to support a second backward wave which interacts with the modulated beam to extract energy therefrom, said wave having frequency characteristics corresponding to the beam modulation and having its maximum iield at the gun end of said second periodic structure, said modulated beam initially interacting with the second wave in the region o-f its maximum iield whereby to provide enhanced interaction, and transducing means disposed between said periodic structures.

12. Apparatus as in claim 11 wherein the transducing means comprises a drift tube.

13. Apparatus as in claim 11 wherein the periodic structures comprise iirst and second helices and wherein the transducing means comprises at least one floating helix.

means comprises a small separation between said periodic structures.

15. A backward-wave amplifier comprising an electron gun serving to project an electron beam, a collector spaced from said gun and serving to intercept said beam, a first periodic structure which propagates the input signal disposed whereby the elds of the propagated signal interact with said beam to thereby modulate the beam in accordance with the signal, input means associated with the collector end of said structure, terminating means associated with the gun end of said structure, a second periodic structure adapted to propagate an output signal as a backward Wave, the maximum iields on said structure occurring at the gun end of said second periodic structure, said structure disposed along the beam whereby the fields of the signal carried by the same interact with the modulated beam to provide an amplified signal corresponding to the input signal, said beam interacting initially with the maximum elds, output means associated with the gun end of said structure, `and terminating means associated with the collector end and serving to attenuate energy traveling towards the collector.

16. Apparatus as in claim 15 wherein the said iirst and second periodic structures comprise helices.

' 17. Apparatus as in claim 15 wherein the said structures are operated at different potentials whereby the bandwidth of the amplifier may be controlled.

14. Apparatus as in claim 11 wherein said transducing 18. Apparatus as in claim 15 wherein the periodic structures have different lengths whereby the bandwidth of said ampliiier may be controlled.

19. A backward-wave amplifier comprising an electron gun, a hollow electron beam projected by said gun, a collector disposed to receive said beam, a first helical structure having its axis coincident with the axis of the beam and serving to propagate an input wave to thereby modulate the electron beam in accordance with said input wave, input means associated with the collector end of said structure and providing means for applying the input signal to the structure, a second helical structure in cascade with said first structure and having its axis coincident with the axis of the beam, said structure serving to propagate the output signal with the maximum fields occurring at the gun end so that the modulated beam from the iirst section initially interacts with maximum fields, output means associated with the gun end of said structure to thereby provide means for removing the output signal from said structure, terminating means associated with ltheicollector end of said helical structure to thereby attenuate energy traveling toward the collector end, and transducing means interposed between said frst and second structure.

20. A backward-wave amplifier as in claim 1 wherein said modulating means comprises a cavity.

21. A backward-wave amplifier as in claim 1 wherein said modulating means comprises a grid.

References Cited in the iile of this patent UNITED STATES PATENTS 2,367,295 Llewellyn Ian. 16, 1945 2,616,990 Knol Nov. 4, 1952 2,637,001 Pierce Apr. 28, 1953 2,653,270 Kompfner Sept. 22, 1953 2,681,951 Warnecke et al. June 22, 1954 2,753,481 Ettenberg July 3, 1956 2,802,136 Lindenblad Aug. 6, 1957 2,814,756 Kenmoku Nov. 26, 1957 2,824,256 Pierce et al Feb. 18, 1958 2,840,752 Cutler et al. June 2-4, 1958 FOREIGN PATENTS 651,516 Great Britain Apr. 4, 1951 699,893 Great Britain Nov. 18, 1953 1,080,027 France May 26, 1954 

